A231775 Triangular array read by rows: row n shows the coefficients of the polynomial u(n) = c(0) + c(1)*x + ... + c(n)*x^(n) which is the denominator of the n-th convergent of the continued fraction [k, k, k, ... ], where k = (x + 1)/(x + 2).

2, 1, 2, 3, 1, 10, 17, 10, 2, 18, 47, 45, 19, 3, 58, 173, 210, 129, 40, 5, 130, 491, 769, 642, 302, 76, 8, 362, 1545, 2850, 2940, 1830, 687, 144, 13, 882, 4391, 9565, 11925, 9315, 4671, 1469, 265, 21, 2330, 12901, 31898, 46195, 43170, 26994, 11294, 3049, 482

Offset

1,1

Comments

Sum of numbers in row n: 3*A002534(n). Left edge: 2*A006131. Right edge: A000045 (Fibonacci numbers).

Links

Table of n, a(n) for n=1..53.

Example

First 3 rows:
2 .... 1
2 .... 3 .... 1
10 ... 17 ... 10 ... 2
First 3 polynomials:  2 + x, 2 + 3*x + x^2, 10 + 17*x + 10*x^2 + 2*x^3.

Mathematica

t[n_] := t[n] = Table[(x + 1)/(x + 2), {k, 0, n}];
b = Table[Factor[Convergents[t[n]]], {n, 0, 10}];
p[x_, n_] := p[x, n] = Last[Expand[Denominator[b]]][[n]];
u = Table[p[x, n], {n, 1, 10}]
v = CoefficientList[u, x]; Flatten[v]

Crossrefs

Cf. A230000, A231774, A000045.

Sequence in context: A111377 A014046 A243919 * A128065 A364933 A361158

Adjacent sequences: A231772 A231773 A231774 * A231776 A231777 A231778

Keyword

nonn,tabf

Author

Clark Kimberling, Nov 13 2013

Status

approved